range of image function is also limited. In monochromatic
images, the lowest value corresponds to black while the highest value corresponds
to white. Brightness values bounded by that range are called
graylevels.

In general, functions may be categorized into:

Type

Domain

Range

Continuous

Continuous

Continuous

Discrete

Discrete

Continuous

Digital

Discrete

Discrete

The quality of the digital image grows in proportion to the image resolution:

Spatial resolution

: given by
the proximity of the image samples in the image plane.

Spectral resolution

: given
by the bandwidth of light frequencies captured by the sensor.

Radiometric resolution

: corresponds
to the number of distinguishable graylevels.

Time resolution

: given by the
interval between time samples at which images are captured.

Image digitization

Image digitization means that a continuous function

f(x,y) is
sampled into a matrix with
M rows and N columns.

Image

quantization assigns to each continuous sample an
integer value.

Two questions should be answered in connection with image function sampling:

The sampling period

:

Based on Shannon sampling theorem. The sampling interval should be chosen in size
such that it is less than half of the smallest interesting detail in the image.

Decreasing the sampling period degrades the image quality. Much of the degradation
is caused by aliasing in the reconstruction of the continuous image function for
display. The display can be improved by the reconstruction algorithm interpolating
brightness values in neighboring pixels.

The geometric arrangements of the sample points

:

Sampling points are ordered on a

grid in the plane.

Grids used in practice are usually

square (rectangular) or hexagonal. Unless
otherwise mentioned, we will always use the rectangular sampling grid.

Each sampling point on the grid is called a

pixel.

Quantization

The transition between continuous values of the image brightness and its digital
equivalent.

CMY – Cyan, Magenta, Yellow – is based on the secondary
colors and is used to construct a subtractive color scheme used for combining inks in color printers. e.g.
yellow subtracts blue from white while a combination of yellow and magenta subtracts
green and blue from white giving red.

The

YIQ
model is useful for TV broadcasting and it is created from RGB as follows:

The

HSI – Hue, Saturation, Intensity – is the most relevant to image processing. Hue refers to the perceived color
or the dominant wavelength and saturation measures the dilution of the color by
white light (dark or light).